// Euler method, can be used as solver.Step.
func (s *BackwardEuler) Step() {
util.AssertMsg(MaxErr > 0, "Backward euler solver requires MaxErr > 0")
t0 := Time
y := M.Buffer()
y0 := cuda.Buffer(VECTOR, y.Size())
defer cuda.Recycle(y0)
data.Copy(y0, y)
dy0 := cuda.Buffer(VECTOR, y.Size())
defer cuda.Recycle(dy0)
if s.dy1 == nil {
s.dy1 = cuda.Buffer(VECTOR, y.Size())
}
dy1 := s.dy1
Dt_si = FixDt
dt := float32(Dt_si * GammaLL)
util.AssertMsg(dt > 0, "Backward Euler solver requires fixed time step > 0")
// Fist guess
Time = t0 + 0.5*Dt_si // 0.5 dt makes it implicit midpoint method
// with temperature, previous torque cannot be used as predictor
if Temp.isZero() {
cuda.Madd2(y, y0, dy1, 1, dt) // predictor euler step with previous torque
M.normalize()
}
torqueFn(dy0)
cuda.Madd2(y, y0, dy0, 1, dt) // y = y0 + dt * dy
M.normalize()
// One iteration
torqueFn(dy1)
cuda.Madd2(y, y0, dy1, 1, dt) // y = y0 + dt * dy1
M.normalize()
Time = t0 + Dt_si
err := cuda.MaxVecDiff(dy0, dy1) * float64(dt)
// adjust next time step
//if err < MaxErr || Dt_si <= MinDt || FixDt != 0 { // mindt check to avoid infinite loop
// step OK
NSteps++
setLastErr(err)
setMaxTorque(dy1)
//} else {
// undo bad step
// util.Assert(FixDt == 0)
// Time = t0
// data.Copy(y, y0)
// NUndone++
//}
}
// Adaptive Heun method, can be used as solver.Step
func (_ *Heun) Step() {
y := M.Buffer()
dy0 := cuda.Buffer(VECTOR, y.Size())
defer cuda.Recycle(dy0)
if FixDt != 0 {
Dt_si = FixDt
}
dt := float32(Dt_si * GammaLL)
util.Assert(dt > 0)
// stage 1
torqueFn(dy0)
cuda.Madd2(y, y, dy0, 1, dt) // y = y + dt * dy
// stage 2
dy := cuda.Buffer(3, y.Size())
defer cuda.Recycle(dy)
Time += Dt_si
torqueFn(dy)
err := cuda.MaxVecDiff(dy0, dy) * float64(dt)
// adjust next time step
if err < MaxErr || Dt_si <= MinDt || FixDt != 0 { // mindt check to avoid infinite loop
// step OK
cuda.Madd3(y, y, dy, dy0, 1, 0.5*dt, -0.5*dt)
M.normalize()
NSteps++
adaptDt(math.Pow(MaxErr/err, 1./2.))
setLastErr(err)
setMaxTorque(dy)
} else {
// undo bad step
util.Assert(FixDt == 0)
Time -= Dt_si
cuda.Madd2(y, y, dy0, 1, -dt)
NUndone++
adaptDt(math.Pow(MaxErr/err, 1./3.))
}
}
func (rk *RK4) Step() {
m := M.Buffer()
size := m.Size()
if FixDt != 0 {
Dt_si = FixDt
}
t0 := Time
// backup magnetization
m0 := cuda.Buffer(3, size)
defer cuda.Recycle(m0)
data.Copy(m0, m)
k1, k2, k3, k4 := cuda.Buffer(3, size), cuda.Buffer(3, size), cuda.Buffer(3, size), cuda.Buffer(3, size)
defer cuda.Recycle(k1)
defer cuda.Recycle(k2)
defer cuda.Recycle(k3)
defer cuda.Recycle(k4)
h := float32(Dt_si * GammaLL) // internal time step = Dt * gammaLL
// stage 1
torqueFn(k1)
// stage 2
Time = t0 + (1./2.)*Dt_si
cuda.Madd2(m, m, k1, 1, (1./2.)*h) // m = m*1 + k1*h/2
M.normalize()
torqueFn(k2)
// stage 3
cuda.Madd2(m, m0, k2, 1, (1./2.)*h) // m = m0*1 + k2*1/2
M.normalize()
torqueFn(k3)
// stage 4
Time = t0 + Dt_si
cuda.Madd2(m, m0, k3, 1, 1.*h) // m = m0*1 + k3*1
M.normalize()
torqueFn(k4)
err := cuda.MaxVecDiff(k1, k4) * float64(h)
// adjust next time step
if err < MaxErr || Dt_si <= MinDt || FixDt != 0 { // mindt check to avoid infinite loop
// step OK
// 4th order solution
madd5(m, m0, k1, k2, k3, k4, 1, (1./6.)*h, (1./3.)*h, (1./3.)*h, (1./6.)*h)
M.normalize()
NSteps++
adaptDt(math.Pow(MaxErr/err, 1./4.))
setLastErr(err)
setMaxTorque(k4)
} else {
// undo bad step
//util.Println("Bad step at t=", t0, ", err=", err)
util.Assert(FixDt == 0)
Time = t0
data.Copy(m, m0)
NUndone++
adaptDt(math.Pow(MaxErr/err, 1./5.))
}
}